Latent variable models are frequently applied to the analysis of responses from test-takers to a set of items, for example, in the context of proficiency testing. Latent variable models that are used for this purpose include item response theory models, diagnostic classification models, multitrait-multimethod models, and discrete mixture distribution models, among others. The National Assessment of Educational Progress (NAEP), the Programme for International Student Assessment (PISA), the Test of English as a Foreign Language (TOEFL), and the Graduate Record Examinations (GRE) are examples of examinations that use item response theory (IRT) or some specific form of multidimensional item response theory (MIRT).